where the function \(U(\mathrm {x})\) , also known as the potential function,
is often convex. The most conventional approaches, random walks Metropolis
Hasting [1]}, often struggle to select a proper
proposal distribution for sampling. As a result, it has been proposed
to consider continuous dynamics which inherently leaves the objective
distribution \(\rho \)  invariant. Probably one of the most well-known
example of these continuous dynamic applications is the over-damped
Langevin diffusion [2]} associated with \(U\) ,
\(dX_{t}=-\nabla U(X_{t})dt+\sqrt{2}dB_{t},\) 
